On the rate-distortion performance of compressive sensing in wireless sensor networks

For many distributed sensing network applications, the goal is to detect temporal and spatial changes in the network. For this purpose, the sensor readings need to be transmitted to the base station (BS) on a regular basis. Since different sensors partially monitor the same spatial region, their sensor readings are highly correlated. Under normal condition, the readings change very slowly that makes them temporally correlated as well. To have an energy-efficient monitoring algorithm, the sensor readings need to be compressed exploiting both spatial and temporal correlations. In many applications of sensor networks, some distortion can be tolerated. In these cases, lossy compression results in compression with higher rates and consequently saves more energy and bandwidth. In this paper, we propose a practical scheme for lossy distributed compression and investigate its rate-distortion limit. The proposed scheme exploiting both spatial and temporal correlations consists of channel coding and compressive sensing. We show that our lossy distributed compression technique achieves the Wyner-Ziv rate distortion for binary sources while it has low computational encoding and decoding complexity.